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Table 3

Brief description of our two models of three-dimensional, X-shape + spiral magnetic fields in galactic disks.

Modela Shape of Referenceb Labels ofc Referenced B r B ϕ B z
poloidal field lines coordinate field lines field

Bd Eq. (87) r1 > 0 z1 (Eq. (88)), ϕ1 (Eq. (70)) Eq. (77), with Eq. (91) Eq. (89) Eq. (68) Eq. (90)

Dd Eq. (31) z1 =  | z1 |   sign  z r1 (Eq. (32)), ϕ1 (Eq. (70)) Eq. (84), with Eq. (35) Eq. (82) Eq. (68) Eq. (83)



The free parameters and functions of models Bd and Dd are the same as those of models B and D, respectively (see Table 1 for the free parameters of the poloidal field and Table 2 for the free parameters and functions describing the azimuthal structure). The only difference concerns the power-law index of field lines asymptotic to the z-axis in model B (now restricted to n ≥ 2) or the r-axis in model D (now set to ).


Prescribed radius or height at which field lines are labeled by their height or radius, respectively, and by their azimuthal angle.


Height or radius of field lines and their azimuthal angle at the reference coordinate.


Radial or vertical field at the reference coordinate as a function of field line labels.

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